Pattern formation
Last update: 21 Apr 2025 21:17
First version: 17 August 1995
Spiral leads me to sleep
I should probably spin off reaction-diffusion models as a separate notebook.
Recommended, close-ups:
- Eric Bonabeau, "From Classical Models of Morphogenesis to
Agent-Based Models of Pattern Formation," Artifical Life
3 (1997): 191--211
- John Tyler Bonner, On
Development
- Janko Gravner and David Griffeath, Snowfakes
[Models of snow-crystal formation]
- David Griffeath, Primordial Soup
Kitchen
- Gemunu H. Gunaratne, David K. Hoffman and Donald J. Kouri,
"Characterization of Natural Patterns," Physical Review E
57 (1998): 5146--5149
- Gemunu H. Gunaratne, Anuradha Ratnaweera and K. Tennekone,
"Emergence of Order in Textured Patterns," patt-sol/9809001
- Lionel Harrison, Kinetic Theory of Living Form
- Paul Manneville, Dissipative Structures and Weak
Turbulence
- Przemyslaw Prusinkiewicz and Mark Hammel, Visual Models of
Morphogenesis: A Guided Tour
- Thimo Rohlf and Stefan Bornholdt
- "Self-organized pattern formation and noise-induced control
from particle computation",
cond-mat/0312366 [Short
version]
- "Morphogenesis by coupled regulatory networks", q-bio.MN/0401024 [Long
version]
- Satoshi Sawai, Peter A. Thomason and Edward C. Cox, "An
autoregulatory circuit for long-range self-organization
in Dictyostelium cell populations", Nature 433
(2005): 323--326
- Vladimir K. Vanang and Irving R. Epstein, "Stationary and
Oscillatory Localized Patterns, and Subcritical Bifurcations", Physical Review
Letters 92 (2004): 128301
- Arthur Winfree
- When Time Breaks Down
- The Geometry of Biological Time
To read:
- Edward R. Abraham, "Sea urchin feeding
fronts", q-bio.PE/0610004
- John A. Adam, Mathematics in Nature: Modeling Patterns in the Natural World
- Mark S. Alber, Yi Jiang and Maria A. Kiskowski, "Lattice gas
cellular automata model for rippling and aggregation in myxobacteria", q-bio/0401014
- Aris, Aronson + Swinney, Patterns and Dynamics in Reactive
Media
- Kenneth A. Brakke, The Motion of a Surface by Its Mean Curvature [1978]
- J. Buceta, Katja Lindenberg, and J. M. R. Parrondo, "Stationary
and Oscillatory Spatial Patterns Induced by Global Periodic Switching," cond-mat/0110542
- A. Carpio, "Wave trains, self-oscillations and synchronization in
discrete media", cond-mat/0506119
- Pierre-Henri Chavanis, "A stochastic Keller-Segel model of
chemotaxis", arxiv:0804.4425
- Elisheva Cohen, David A. Kessler and Herbert Levine,
"Fluctuation-Regularized Front Propagation Dynamics in Reaction-Diffusion
Systems", Physical Review
Letters 94 (2005): 158302
- Pierre Collet and Jean-Pierre Eckmann, Instabilities and Fronts in Extended Systems
- Catherine Crawford and Hermann Riecke, "Oscillon-Type Structures
and Their Interaction in a Swift-Hohenberg Model," patt-sol/9804005
- Karen E. Daniels, Christian Beck and Eberhard Bodenschatz, "Defect
turbulence and generalized statistical mechanics,"
cond-mat/0302623
- Jörn Davidsen, Ronaldo Erichsen, Raymond Kapral and Hughes
Chaté, "From ballistic to Brownian vortex motion in complex oscillatory
media", Physical Review Letters 93 (2004): 018305
= nlin.PS/0410033
- Epstein and Pojman, An Introduction to Nonlinear Chemical
Dynamics
- Amatzia Genin, Jules S. Jaffe, Ruth Reef, Claudio Richter, Peter
J. S. Franks, "Swimming Against the Flow: A Mechanism of Zooplankton
Aggregation", Science 308
(2005): 860--862
- Solomon W. Golomb, Polyominoes illus. Waren
Lushbaugh
- Nigel Goldenfeld, Pak Yuen Chan and john Veysey, "Dynamics of
Precipitation Pattern Formation at Geothermal Hot
Springs", Physical Revieew
Letters 96 (2006): 254501
= nlin.PS/0601028
- Roman O. Grigoriev and Andreas Handel, "Nonnormality and the
localized control of extended systems," nlin.PS/0207023
- Ramon Grima, "Strong-coupling dynamics of a multi-cellular
chemotactic system", q-bio.CB/0505004
- Peter Grindrod, Theory and Application of Reaction Diffusion
Equations: Patterns and Waves
- Kevin Hall and Leon Glass, "How to Tell a Target from a Spiral:
The Two Probe Problem," Physical Review Letters
82 (1999): 5164--5167
- Rebecca Hoyle, Pattern Formation: An Introduction to
Methods
- Lukas Jahnke and Jan W. Kantelhardt, "Comparison of models and
lattice-gas simulations for Liesegang
patterns", arxiv:0803.3634
- Y. Kuramoto, Chemical Oscillations, Waves, and
Turbulence [Now re-issued as a cheap Dover paperback]
- Julio Largo, Piero Tartaglia, Francesco Sciortino, "Effective
non-additive pair potential for lock-and-key interacting particles: the role of
the limited
valence", cond-mat/0703383
- Men Li, Heimo Schnablegger and Stephen Mann, "Coupled Synthesis
and Self-Assembly of Nanoparticles to Give Structures with Controlled
Organization," Nature 402 (1999): 393--395
- Markus Loecher, Noise Sustained Patterns: Fluctuations and
Nonlinearities
- Juan M. Lopez and Henrik J. Jensen, "Generic model of
morphological changes in growing colonies of fungi," cond-mat/0110509
- Paul Manneville, Instabilities, Chaos and Turbulence
- Jonathan H. McCoy, Will Brunner, Werner Pesch and Eberhard Bodenschatz, "Self-Organization of Topological Defects due to Applied Constraints",
Physical Review Letters 101 (2008): 254102
- K. R. Mecke and D. stoyan (eds.), Statistical Physics and
Spatial Statistics: The Art of Analyzing and Modeling Spatial Structures and
Pattern Formation
- Girish Nathan and Gemunu Gunaratne, "Set of measures to analyze the
dynamics of nonequilibrium structures",
Physical Review
E 71 (2005): 035101(R)
- David R. Nelson, Defects and Geometry in Condensed Matter
Physics
- Wouter-Jan Rappel, Alastair Nicol, Armand Sarkissian, Herbert
Levine and William F. Loomis, "Self-Organized Vortex State in Two-Dimensional
Dictyostelium Dynamics," patt-sol/9811001
- D. Reguera (ed.), Coherent Structures in Complex
Systems
- Hermann Riecke, "Localized Structures in Pattern-Forming
Systems," patt-sol/9810002
- Jori E. Ruppert-Felsot, Olivier Praud, Eran Sharon, Harry
L. Swinney, "Extraction of coherent structures in a rotating turbulent flow
experiment", physics/0410161
- J. M. Sancho and Jordi Garcia-Ojalvo, "Noise-Induced Order
in Extended Systems: A Tutorial", cond-mat/0608511
- Sumithra Sankararaman, Gautam I. Menon and P. B. Sunil Kumar,
"Self-organized pattern formation in motor-microtubule mixtures", Physical Review
E 70 (2004): 031905
- Smoller, Shock Waves and Reaction-Diffusion Equations
- Swinney and Krinsky (eds). Waves and Patterns (a.k.a.
Phyisca D 49)
- Uwe C. Tauber, Martin Howard and Benjamin P. Vollmayr-Lee,
"Applications of field-theoretic renormalization group methods to
reaction-diffusion problems", Journal of Physics
A 38 (2005): 79--131 = cond-mat/0501678
- Steffen Trimper and Knud Zabrocki, "Memory Driven Pattern
Formation", cond-mat/0406269
- 25 Years of Non-Equilibrium Statistical Mechanics:
Proceedings, Sitges, Barcelona, 1994
- Paul Umbanhowar, Pattern Formation in
Granular Materials
- Daniel Walgraef, Spatio-temporal Pattern Formation: with
Examples from Physics, Chemistry and Materials Science
- Stephen Whitelam and Phillip L. Geissler, "Cluster algorithm for
pairwise-interacting particles", cond-mat/0508100 [with special
application to self-assembling particle systems]
- Lancelot Whyte (ed.). Aspects of Form
- H. S. Wio, S. Bouzat and B. von Haeften, "Stochastic Resonance in
Spatially Extended Systems: The Role of Far from Equilibrium Potentials," cond-mat/0109452